We consider the problem of constructing a microlocal logarithm and a normal form for an elliptic semi-classical Fourier integral operator near a fixed point of the corresponding canonical transformation. In [Ia] the canonical ...

We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.

The Jansen-Heß operator is an approximate (pseudo-)relativistic no-pair Hamiltonian in the Furry picture which is used in the physics literature to describe heavy atoms. Within the single-particle Coulomb model we prove ...

To study the location of poles for the acoustic scattering matrix for two strictly convex obstacles with smooth boundaries, one uses an approximation of the quantized billiard operator M along the trapped ray between the ...